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In a Young's double-slit experiment with slits A and B, a thin film of thickness t and refractive index mu is introduced in front of slit A. With fringe width b, in which direction does the central maximum shift and by how much?

1. towards A
2. towards B
3. by t*(mu - 1)*b/lambda
4. by mu*t*b/lambda

Correct answer: towards A

Solution

The extra optical path (mu - 1)*t added on the A side must be balanced by a geometric path on the A side, so the central maximum shifts toward A. (The magnitude is (mu - 1)*t*b/lambda, but among these options the correct one describing the shift is 'towards A'.)

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